n choose k proof

[intervade]

Ok, so I'm told to prove n C k = n C (k-1) now, I know that this is equivalent to

n!/k!(n-k)! = n!/(k-1)!(n-k+1)! but where do I go from there? I'm not really positive on how to manipulate these, I tried multiplying by k/k on the RHS and I get(I think)

n!(k)/(k)(k-1)!(n-k+1)! which equals n!(k)/k!(n-k+1)! but I get stuck here.

 

[mmm4444bot]

I'm told to prove n C k = n C (k-1) Are you sure?

5 C 4 = 5

5 C 3 = 10

They're not equal.